For the past many years, the design of the photonic crystals of complicated 3-D structures was usually made by suing the finite-difference time-domain (FD-TD) method. The method is very slow when an electrically large-scaled problem is characterized. Also, quite often, the problem is considered in the frequency domain for a spectrum of the light waves. Although the other methods see more details in the later text are also applicable, but they are either less efficient in speed and accuracy, or applicable to time domain. The frequency domain work will have to require the Fourier transform and additional time and efforts are required. This work explores applying the volume integral equations for characterizing and designing the 2D and even 3D structured photonic crystals. Because of many different choices of the basis functions for the volume cells, the approach will be very flexible in handling many different types of photonic crystals of various geometrical structures. Most importantly, the proposed approach can be accelerated by the fast solver so that many theoretical untouchable large scaled problems to become solve-able and previously slow converged problems to be fast in convergence and accurate in solution.